Logic says that turning it off is going to give you better battery life. In any case, it couldn't make the battery life worse.

I can only speak for the iPhone which does scan for new networks but it isn't a constant thing. It will only happen while you are using the phone. As soon as you lock it then it will only connect to known networks intermittently for email, push notifications etc. I'd imagine other phones kill the connection when the phone is idle, too.

I used to turn mine off but I can't say I have noticed a difference. The inconvenience and forgetting to turn it back on (chewing through my data allowance whilst at home) persuaded me to leave it on.

If you know you won't be getting to a power source any time soon and you're a little worried then disable push notifications, turn the screen brightness down, disable 3G and then turn off wi-fi.

I turn it off overnight and when I'm out the house as I do notice a difference in battery life. I would say it depends on what phone you have. Android phones have widgets which let you turn on and off WiFi with one touch, iPhones are a little more complicated but have better battery life anyway.